The New Sudoku Players' Forum

[mith]

Code: Select all

+-------+-------+-------+
| 9 . . | . . . | . . . |
| . . 8 | 7 . . | . . 6 |
| . 5 . | . 4 . | . 3 . |
+-------+-------+-------+
| . 3 . | . 5 . | . 2 . |
| . . 9 | 6 . . | . . 8 |
| . . . | . . 9 | 4 . . |
+-------+-------+-------+
| . 4 . | . 1 . | . 5 . |
| . . 6 | 8 . . | . . . |
| 1 . . | . . . | 2 . . |
+-------+-------+-------+
9..........87....6.5..4..3..3..5..2...96....8.....94...4..1..5...68.....1.....2..

[rjamil]

Let start solving from scratch:

Code: Select all

 +---------------------+--------------------+---------------------+
 | 9      1267   12347 | 1235  2368  123568 | 1578   1478   12457 |
 | 234    12     8     | 7     239   1235   | 159    149    6     |
 | 267    5      127   | 129   4     1268   | 1789   3      1279  |
 +---------------------+--------------------+---------------------+
 | 4678   3      147   | 14    5     1478   | 1679   2      179   |
 | 2457   127    9     | 6     237   12347  | 1357   17     8     |
 | 25678  12678  1257  | 123   2378  9      | 4      167    1357  |
 +---------------------+--------------------+---------------------+
 | 2378   4      237   | 239   1     2367   | 36789  5      379   |
 | 2357   279    6     | 8     2379  23457  | 1379   1479   13479 |
 | 1      789    357   | 3459  3679  34567  | 2      46789  3479  |
 +---------------------+--------------------+---------------------+

1) HP: 34 @ r1c3 r2c1 in Box 1;
2) HP: 35 @ r5c7 r6c9 in Box 6;
3) HP: 68 @ r7c7 r9c8 in Box 9;
4) SF: 5 @ r258c167 Row wise;
5) SF: 6 @ r347c167 Row wise;
6) SF: 8 @ r347c167 Row wise;
7) HP: 68 @ r1c5 r3c6 in Box 2;
8) HP: 68 @ r4c1 r6c2 in Box 4;
9) SF: 9 @ r347c479 Row wise;
10) HT: 689 @ r9c258 in Row 9;
11) HT: 689 @ r347c7 in Column 7;
12) JF: 7 @ r3479c1369 Row wise;
13) NS: 2 @ r6c1;
14) NP: 17 @ r5c28 in Row 5;
15) HT: 678 @ r6c258 in Row 6;
16) NT: 345 @ r258c1 in Column 1;
17) HP: 78 @ r4c6 r6c5 in Box 5;
18) LC (Type 1 Pointing): 1 @ r456c4;
19) SF: 1 @ r346c349 Row wise;
20) SF: 2 @ r258c256 Row wise;
21) HP: 25 @ r1c49 in Row 1;
22) LC (Type 1 Pointing): 4 @ r123c8;
23) JF: 3 @ r1679c3469 Row wise;
24) NS: 4 @ r8c9;
25) HT: 349 @ r2c158 in Row 2;

Code: Select all

 +--------------+----------------+---------------------+
 | 9   167  34  | 25   68    13  | (17)  148-7  25     |
 | 34  12   8   | 7    39    125 | 15    49     6      |
 | 67  5    127 | 29   4     68  | 89    3      (1)279 |
 +--------------+----------------+---------------------+
 | 68  3    147 | 14   5     78  | 69    2      (1)79  |
 | 45  17   9   | 6    23    24  | 35    (17)   8      |
 | 2   68   15  | 13   78    9   | 4     67     35     |
 +--------------+----------------+---------------------+
 | 78  4    237 | 239  1     367 | 68    5      379    |
 | 35  279  6   | 8    2379  25  | 137   179    4      |
 | 1   89   357 | 345  69    347 | 2     68     37     |
 +--------------+----------------+---------------------+

26) W-Wing: 17 @ r1c7 r5c8 SL 1 @ r34c9 => -7 @ r1c8;

Code: Select all

 +----------------+--------------------+---------------------+
 | 9     167  34  | 25   68      13    | 17     148    25    |
 | 34    12   8   | 7    39      125   | 15     49     6     |
 | (67)  5    127 | 29   4       (68)  | 89     3      129-7 |
 +----------------+--------------------+---------------------+
 | 68    3    147 | 14   5       (78)  | 69     2      179   |
 | 45    17   9   | 6    23      24    | 35     17     8     |
 | 2     68   15  | 13   78      9     | 4      67     35    |
 +----------------+--------------------+---------------------+
 | 78    4    237 | 239  1       36[7] | 68     5      3[7]9 |
 | 35    279  6   | 8    23[7]9  (25)  | 13[7]  1[7]9  (4)   |
 | 1     89   357 | 345  69      34[7] | 2      68     3[7]  |
 +----------------+--------------------+---------------------+

27) XY-Wing Transport: 678 @ r3c16 r4c6 ERI 7 @ b8r8c6 ERI 7 @ b9r8c9 => -7 @ r3c9;
28) HS: 7 @ r1c7 in Box 3; and

Code: Select all

 +----------------+-----------------+--------------+
 | 9     16   34  | 25   68    13   | 7   148  25  |
 | 34    12   8   | 7    39    125  | 15  49   6   |
 | 67    5    127 | 29   4     68   | 89  3    129 |
 +----------------+-----------------+--------------+
 | 68    3    147 | 14   5     78   | 69  2    179 |
 | (45)  17   9   | 6    23    (24) | 35  17   8   |
 | 2     68   15  | 13   78    9    | 4   67   35  |
 +----------------+-----------------+--------------+
 | 78    4    237 | 239  1     367  | 68  5    379 |
 | 3-5   279  6   | 8    2379  (25) | 13  179  4   |
 | 1     89   357 | 345  69    347  | 2   68   37  |
 +----------------+-----------------+--------------+

29) XY-Wing: 245 @ r5c16 r8c6 => -5 @ r8c1; stte

R. Jamil

[Cenoman]

I'm aware that's not the expectation. Just the usual kind of fun !
One step:

Code: Select all

 +-------------------------+-------------------------+------------------------+
 |  9       1267    34     |  1235   2368   123568   |  1578   1478  Y12457   |
 | z34      12      8      |  7      239    1235     |  159  Ie19-4   6       |
 |  267     5       127    | a129    4     B1268     | A1789   3     t1279    |
 +-------------------------+-------------------------+------------------------+
 |VD4678    3      U147    | U14     5     C1478     |  1679   2     U179     |
 | W2457    127     9      |  6      237    12347    | W35     17     8       |
 |  25678   12678   1257   |  123    2378   9        |  4      167   X35      |
 +-------------------------+-------------------------+------------------------+
 | E2378    4       237    | b239    1      2367     |  68     5     c379     |
 |  2357   G279     6      |  8      2379   23457    |  1379 Hd1479   13479   |
 |  1      F789     357    |  3459   3679   34567    |  2      68     3479    |
 +-------------------------+-------------------------+------------------------+

Double Kraken: row (9)r3c479 & column (4)r245c1
(9)r3c4 - r7c4 = r7c9 - r8c8 = (9)r2c8
(9-8)r3c7 = r3c6 - r4c6 = r4c1 - r7c1 = (8-9)r9c2 = r8c2 - r8c8 = (9)r2c8
(9)r3c9 - [(9=174)r4c349 - r4c1 = (45)r5c17 - r6c9 = (52)r13c9] = (4)r2c1
=> -4 r2c8; lclste
(embedded chain tagged U...Y from left to right)

Same as a net:

Hidden Text: Show

Code: Select all

(9)r3c4 - r7c4 = r7c9 - r8c8 = (9)r2c8 *
 ||
(9-8)r3c7 = r3c6 - r4c6 = r4c1 - r7c1 = (8-9)r9c2 = r8c2 - r8c8 = (9)r2c8 *
 ||
 ||    (9=174)r4c349 - - - (4)r4c1
 ||    /                    ||
(9)r3c9                    (4)r2c1 *
       \                    ||
       (25)r13c9 = r6c9 - (54)r5c17
------------------
=> -4 r2c8; lclste

[Leren]

My solution was basically the same as rjamil's except that you can dispense with moves 26 - 28 and go straight to the XY Wing. stte from there.

Leren

[mith]

My solution was basically the same as rjamil's except that you can dispense with moves 26 - 28 and go straight to the XY Wing. stte from there.

Leren

Likewise (and 23 can be done as an SF in columns). Cenoman's one step is awfully impressive though.

[Leren]

Hodoku's solution was similar except that they also included one extraneous W Wing.

Leren

[denis_berthier]

Code: Select all

+-------+-------+-------+
| 9 . . | . . . | . . . |
| . . 8 | 7 . . | . . 6 |
| . 5 . | . 4 . | . 3 . |
+-------+-------+-------+
| . 3 . | . 5 . | . 2 . |
| . . 9 | 6 . . | . . 8 |
| . . . | . . 9 | 4 . . |
+-------+-------+-------+
| . 4 . | . 1 . | . 5 . |
| . . 6 | 8 . . | . . . |
| 1 . . | . . . | 2 . . |
+-------+-------+-------+
9..........87....6.5..4..3..3..5..2...96....8.....94...4..1..5...68.....1.....2..

As pure Subsets are not enough, I added bivalue chains. Two short ones are enough.

Hidden Text: Show

***********************************************************************************************
*** SudoRules 20.1.s based on CSP-Rules 2.1.s, config = BC+O+SFin
*** Using CLIPS 6.32-r770
***********************************************************************************************
223 candidates, 1451 csp-links and 1451 links. Density = 5.86%
hidden-pairs-in-a-block: b9{r7c7 r9c8}{n6 n8} ==> r9c8 ≠ 9, r9c8 ≠ 7, r9c8 ≠ 4, r7c7 ≠ 9, r7c7 ≠ 7, r7c7 ≠ 3
hidden-pairs-in-a-block: b6{r5c7 r6c9}{n3 n5} ==> r6c9 ≠ 7, r6c9 ≠ 1, r5c7 ≠ 7, r5c7 ≠ 1
hidden-pairs-in-a-block: b1{r1c3 r2c1}{n3 n4} ==> r2c1 ≠ 2, r1c3 ≠ 7, r1c3 ≠ 2, r1c3 ≠ 1
swordfish-in-columns: n8{c2 c5 c8}{r9 r6 r1} ==> r6c1 ≠ 8, r1c7 ≠ 8, r1c6 ≠ 8
swordfish-in-columns: n9{c2 c5 c8}{r8 r9 r2} ==> r9c9 ≠ 9, r9c4 ≠ 9, r8c9 ≠ 9, r8c7 ≠ 9, r2c7 ≠ 9
hidden-triplets-in-a-column: c7{n6 n8 n9}{r4 r7 r3} ==> r4c7 ≠ 7, r4c7 ≠ 1, r3c7 ≠ 7, r3c7 ≠ 1
swordfish-in-columns: n5{c3 c4 c9}{r6 r9 r1} ==> r9c6 ≠ 5, r6c1 ≠ 5, r1c7 ≠ 5, r1c6 ≠ 5
swordfish-in-columns: n6{c2 c5 c8}{r6 r1 r9} ==> r9c6 ≠ 6, r6c1 ≠ 6, r1c6 ≠ 6
hidden-pairs-in-a-block: b2{r1c5 r3c6}{n6 n8} ==> r3c6 ≠ 2, r3c6 ≠ 1, r1c5 ≠ 3, r1c5 ≠ 2
hidden-pairs-in-a-block: b4{r4c1 r6c2}{n6 n8} ==> r6c2 ≠ 7, r6c2 ≠ 2, r6c2 ≠ 1, r4c1 ≠ 7, r4c1 ≠ 4
hidden-triplets-in-a-row: r9{n6 n8 n9}{c5 c8 c2} ==> r9c5 ≠ 7, r9c5 ≠ 3, r9c2 ≠ 7
biv-chain[3]: r8n5{c6 c1} - r5n5{c1 c7} - c7n3{r5 r8} ==> r8c6 ≠ 3
jellyfish-in-columns: n7{c2 c7 c5 c8}{r5 r1 r8 r6} ==> r8c9 ≠ 7, r8c6 ≠ 7, r8c1 ≠ 7, r6c3 ≠ 7, r6c1 ≠ 7, r5c6 ≠ 7, r5c1 ≠ 7, r1c9 ≠ 7
naked-single ==> r6c1 = 2
naked-pairs-in-a-row: r5{c2 c8}{n1 n7} ==> r5c6 ≠ 1, r5c5 ≠ 7
hidden-pairs-in-a-block: b5{r4c6 r6c5}{n7 n8} ==> r6c5 ≠ 3, r4c6 ≠ 4, r4c6 ≠ 1
whip[1]: b5n1{r6c4 .} ==> r1c4 ≠ 1, r3c4 ≠ 1
naked-triplets-in-a-column: c1{r2 r5 r8}{n3 n4 n5} ==> r7c1 ≠ 3
naked-triplets-in-a-row: r6{c3 c4 c9}{n5 n1 n3} ==> r6c8 ≠ 1
swordfish-in-rows: n1{r3 r4 r6}{c3 c9 c4} ==> r8c9 ≠ 1, r1c9 ≠ 1
swordfish-in-columns: n3{c1 c5 c7}{r8 r2 r5} ==> r8c9 ≠ 3, r5c6 ≠ 3, r2c6 ≠ 3
naked-single ==> r8c9 = 4
naked-triplets-in-a-row: r2{c2 c6 c7}{n1 n2 n5} ==> r2c8 ≠ 1, r2c5 ≠ 2
finned-x-wing-in-rows: n2{r2 r8}{c2 c6} ==> r7c6 ≠ 2
swordfish-in-rows: n2{r2 r5 r8}{c2 c6 c5} ==> r1c6 ≠ 2, r1c2 ≠ 2
hidden-pairs-in-a-row: r1{n2 n5}{c4 c9} ==> r1c4 ≠ 3
biv-chain[3]: b5n3{r6c4 r5c5} - r2c5{n3 n9} - c4n9{r3 r7} ==> r7c4 ≠ 3
naked-pairs-in-a-column: c4{r3 r7}{n2 n9} ==> r1c4 ≠ 2
stte

I don't know why, but I also thought of trying Oddagons instead of bivalue-chains, and there's a final one, after only Subsets. Of course, this is not a very rational solution, as the bivalue-chains in the first resolution path are much simpler.

Hidden Text: Show

(solve "9..........87....6.5..4..3..3..5..2...96....8.....94...4..1..5...68.....1.....2..")
***********************************************************************************************
*** SudoRules 20.1.s based on CSP-Rules 2.1.s, config = O+SFin
*** Using CLIPS 6.32-r770
***********************************************************************************************
223 candidates, 1451 csp-links and 1451 links. Density = 5.86%
hidden-pairs-in-a-block: b9{r7c7 r9c8}{n6 n8} ==> r9c8 ≠ 9, r9c8 ≠ 7, r9c8 ≠ 4, r7c7 ≠ 9, r7c7 ≠ 7, r7c7 ≠ 3
hidden-pairs-in-a-block: b6{r5c7 r6c9}{n3 n5} ==> r6c9 ≠ 7, r6c9 ≠ 1, r5c7 ≠ 7, r5c7 ≠ 1
hidden-pairs-in-a-block: b1{r1c3 r2c1}{n3 n4} ==> r2c1 ≠ 2, r1c3 ≠ 7, r1c3 ≠ 2, r1c3 ≠ 1
swordfish-in-columns: n8{c2 c5 c8}{r9 r6 r1} ==> r6c1 ≠ 8, r1c7 ≠ 8, r1c6 ≠ 8
swordfish-in-columns: n9{c2 c5 c8}{r8 r9 r2} ==> r9c9 ≠ 9, r9c4 ≠ 9, r8c9 ≠ 9, r8c7 ≠ 9, r2c7 ≠ 9
hidden-triplets-in-a-column: c7{n6 n8 n9}{r4 r7 r3} ==> r4c7 ≠ 7, r4c7 ≠ 1, r3c7 ≠ 7, r3c7 ≠ 1
swordfish-in-columns: n5{c3 c4 c9}{r6 r9 r1} ==> r9c6 ≠ 5, r6c1 ≠ 5, r1c7 ≠ 5, r1c6 ≠ 5
swordfish-in-columns: n6{c2 c5 c8}{r6 r1 r9} ==> r9c6 ≠ 6, r6c1 ≠ 6, r1c6 ≠ 6
hidden-pairs-in-a-block: b2{r1c5 r3c6}{n6 n8} ==> r3c6 ≠ 2, r3c6 ≠ 1, r1c5 ≠ 3, r1c5 ≠ 2
hidden-pairs-in-a-block: b4{r4c1 r6c2}{n6 n8} ==> r6c2 ≠ 7, r6c2 ≠ 2, r6c2 ≠ 1, r4c1 ≠ 7, r4c1 ≠ 4
hidden-triplets-in-a-row: r9{n6 n8 n9}{c5 c8 c2} ==> r9c5 ≠ 7, r9c5 ≠ 3, r9c2 ≠ 7
jellyfish-in-columns: n7{c2 c7 c5 c8}{r5 r1 r8 r6} ==> r8c9 ≠ 7, r8c6 ≠ 7, r8c1 ≠ 7, r6c3 ≠ 7, r6c1 ≠ 7, r5c6 ≠ 7, r5c1 ≠ 7, r1c9 ≠ 7
naked-single ==> r6c1 = 2
naked-pairs-in-a-row: r5{c2 c8}{n1 n7} ==> r5c6 ≠ 1, r5c5 ≠ 7
hidden-pairs-in-a-block: b5{r4c6 r6c5}{n7 n8} ==> r6c5 ≠ 3, r4c6 ≠ 4, r4c6 ≠ 1
whip[1]: b5n1{r6c4 .} ==> r1c4 ≠ 1, r3c4 ≠ 1
naked-triplets-in-a-column: c1{r2 r5 r8}{n3 n4 n5} ==> r7c1 ≠ 3
naked-triplets-in-a-row: r6{c3 c4 c9}{n5 n1 n3} ==> r6c8 ≠ 1
swordfish-in-rows: n1{r3 r4 r6}{c3 c9 c4} ==> r8c9 ≠ 1, r1c9 ≠ 1
swordfish-in-columns: n3{c1 c5 c7}{r8 r2 r5} ==> r8c9 ≠ 3, r8c6 ≠ 3, r5c6 ≠ 3, r2c6 ≠ 3
naked-single ==> r8c9 = 4
naked-triplets-in-a-row: r2{c2 c6 c7}{n1 n2 n5} ==> r2c8 ≠ 1, r2c5 ≠ 2
finned-x-wing-in-rows: n2{r2 r8}{c2 c6} ==> r7c6 ≠ 2
swordfish-in-rows: n2{r2 r5 r8}{c2 c6 c5} ==> r1c6 ≠ 2, r1c2 ≠ 2
hidden-pairs-in-a-row: r1{n2 n5}{c4 c9} ==> r1c4 ≠ 3
oddagon[7]: r5c6{n2 n4},r5n4{c6 c1},r5c1{n4 n5},c1n5{r5 r8},r8n5{c1 c6},r8c6{n5 n2},c6n2{r8 r5} ==> r5c6 ≠ 2
stte

[pjb]

One can start with the swordfishes, but I used two MSLSs:

16 cell Truths: r1258 c2578
16 links: 678r1, 9r2, 7r5, 79r8, 12c2, 23c5, 135c7, 14c8
17 eliminations

23 cell Truths: r12568 c12578
23 links: 68r1, 39r2, 3r5, 68r6, 39r8, 245c1, 127c2, 27c5, 157c7, 147c8
8 eliminations

this is the reuslting state:

Code: Select all

 9       1267    34     | 1235   68     1235   | 157    1478   1245   
 4-3     12      8      | 7      39     125    | 15     49     6     
 67      5       127    | 129    4      68     | 89     3      1279   
------------------------+----------------------+---------------------
 68      3       147    | 14     5      1478   | 69     2      179   
 245     127     9      | 6      237    124    | 35     17     8     
 25      68      125    | 123    78     9      | 4      67     35     
------------------------+----------------------+---------------------
 78      4       237    | 239    1      2367   | 68     5      379   
 235     279     6      | 8      2379   245    | 137    1479   14     
 1       89      357    | 345    69     3457   | 2      68     347   


Then a Kraken box:
(9-4)r2c8 = (4)r2c1
(9-)r3c7 = r1c8 - (8=6)r1c5 - (6=9)r9c5 - (9=3)r2c5 - (3=4)r2c1
(9-2)r3c9 = (2-5)r1c9 = (5-3)r6c9 = (3-5)r5c7 = (5-4)r5c1 = (4)r2c1 => r2c1=4; stte

Phil